项目拟通过直接数值模拟的方法研究重力驱动下圆球颗粒在流体中自由运动的两大宏观特性：团聚行为和自相似结构。这里的自由运动包括颗粒的沉降（颗粒密度大于流体密度）和上升（颗粒密度小于流体密度）。对它们的研究将有助于揭示大量颗粒在重力背景下相互作用的本质，不仅是工业生产的需求，也是完善和发展离散颗粒多相流理论的需要。为了研究以上的宏观特性，首先通过直接数值模拟和PIV实验研究双圆球颗粒在流体中相互作用的微观结构及动力学特性。在此基础上，考察惯性区域内[颗粒雷诺数量级为O(10)~O(10^2)]颗粒群的团聚，从“虚拟湍流”的角度出发探索团聚的机理，研究团聚的发生条件，建立团聚后颗粒群宏观速度的预测模型；考察Stokes区域（颗粒雷诺数<<1），Oseen区域[颗粒雷诺数≲O(1)]和惯性区域内颗粒群的自相似结构，构建这一结构的扩散模型，考察自相似结构的时间尺度和空间尺度，并揭示其标度率。

In this project direct numerical simulation (DNS) is carried out to study the cluster and self-similar structure of spherical particles which are freely falling (particle density greater than fluid density) or ascending (particle density smaller than fluid density) under gravity. The particle cluster is one of the most important dynamical features of particles, as well as the self-similar structure. This study aims to reveal the mechanism of particle mutual interactions in the cases of a large number of particles driven by gravity, which is fundamental from the viewpoint of both multiphase flow theory and industrial applications. First of all, both the DNS and PIV are employed to investigate the interactions of two spherical particles freely moving in a fluid. The investigation will focus on the microstructures as well as the dynamical features of these two particles. On this basis, the DNS is conduced to study the cluster of particles in the inertial regime [particle Reynolds number O(10)~O(10^2)]. The effort will be made to explore the mechanism of particle cluster from the viewpoint of “pseudo turbulence”. In addition, the study aims to present a model which is able to predict the enhanced averaged velocity of particles due to clusters. On the other.hand, the self-similar structures of particles in the Stokes regime (particle Reynolds number << 1), Oseen regime [particle Reynolds number ≲ O(1)] and inertial regime are taken into account. Through DNS a diffusive model is developed to characterize the self-similar structure when the fluid inertia can not be neglected. Then the scaling law is revealed by determining the geometry and time scales related to the self-similar structure.